Unique Solvability of a Coupling Problem for Entire Functions
نویسندگان
چکیده
منابع مشابه
Unique solvability of a coupling problem for entire functions
We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance for the integration of certain nonlinear wave equations. Results Let σ be a discrete set of nonzero reals such that the sum ∑
متن کاملA note on unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...
متن کاملAn extremal problem for a class of entire functions
Let f be an entire function of the exponential type, such that the indicator diagram is in [−iσ, iσ ], σ > 0. Then the upper density of f is bounded by cσ , where c≈ 1.508879 is the unique solution of the equation log (√ c2 + 1 + c) =√1 + c−2. This bound is optimal. To cite this article: A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Académie des sciences. Publishe...
متن کاملSolvability and the Unique Solvability of a Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations
Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem u′(t) = F (u)(t), u(a)− λu(b) = h(u) are established, where F : C([a, b];R) → L([a, b];R) is a continuous operator satisfying the Carathéodory condition, h : C([a, b];R) → R is a continuous functional, and λ ∈ R+. 2000 Mathematics Subject Classification: 34K10.
متن کاملA Coupling Problem for Entire Functions and Its Application to the Long-time Asymptotics of Integrable Wave Equations
We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the case where the underlying isospectral problem has purely discrete spectrum. To this end we introduce a natural coupling problem for entire functions which serves as a replacement for the usual Riemann–Hilbert approach, which does not work for these kind of problems. As a prototypical example...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2017
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-017-9394-2